Efficient reduced-basis approximation of scalar nonlinear time-dependent convection-diffusion problems, and extension to compressible flow problems
Citable URI:
http://hdl.handle.net/1721.1/39214
| Title: | Efficient reduced-basis approximation of scalar nonlinear time-dependent convection-diffusion problems, and extension to compressible flow problems |
| Author: | Men, Han (Han Abby) |
| Other Contributors: | Massachusetts Institute of Technology. Computation for Design and Optimization Program. |
| Advisor: | Jamie Peraire. |
| Department: | Massachusetts Institute of Technology. Computation for Design and Optimization Program. |
| Publisher: | Massachusetts Institute of Technology |
| Issue Date: | 2006 |
| Abstract: |
In this thesis, the reduced-basis method is applied to nonlinear time-dependent convection-diffusion parameterized partial differential equations (PDEs). A proper orthogonal decomposition (POD) procedure is used for the construction of reduced-basis approximation for the field variables. In the presence of highly nonlinear terms, conventional reduced-basis would be inefficient and no longer superior to classical numerical approaches using advanced iterative techniques. To recover the computational advantage of the reduced-basis approach, an empirical interpolation approximation method is employed to define the coefficient-function approximation of the nonlinear terms. Next, the coefficient-function approximation is incorporated into the reduced-basis method to obtain a reduced-order model of nonlinear time-dependent parameterized convection-diffusion PDEs. Two formulations for the reduced-order models are proposed, which construct the reduced-basis space for the nonlinear functions and residual vector respectively. Finally, an offline-online procedure for rapid and inexpensive evaluation of the reduced-order model solutions and outputs, as well as associated asymptotic a posterior error estimators are developed. (cont.) The operation count for the online stage depends only on the dimension of our reduced-basis approximation space and the dimension of our coefficient-function approximation space. The extension of the reduced-order model to a system of equations is also explored. |
| Description: | Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2006. Includes bibliographical references (p. 61-65). |
| URI: | http://hdl.handle.net/1721.1/39214 |
| Keywords: | Computation for Design and Optimization Program. |
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